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### Fraction complete summary

1. 1. CompanyLOGOwww.company.comFRACTIONSITI NURAININUR ENDAH P.ICHWANU TAFFILIATIS S. R.
2. 2. CompanyLOGOwww.company.comINTRODUCTION
3. 3. CompanyLOGOwww.company.comDo you still remember about the definition offactor?factor of a number is natural number that candivide a number till nothing remainderDo you still remember about the definition ofGCD?Greatest Common Divisor / Greatest CommonFactor is the greatest factor that satisfied for twoor more than two numbers.
4. 4. CompanyLOGOwww.company.com• Do you still remember about the definition ofLCM?Least Common Multiple (LCM) is the leastmultiple that satisfied for two or more than twonumbers.• How about if natural number can’t divide anumber till nothing remainder?Who am I??
5. 5. CompanyLOGOwww.company.comLearning Objective: Students are able to:• Simplify fraction.• Change a mixed number into fractions and itsinverse.• Compare fractions and order the fractions.• Write a fraction in a decimal or a percent form,• Operate fractions and apply it in everyday life.• Explain properties of the operations and itsapplication in everyday life
6. 6. CompanyLOGOwww.company.com
7. 7. CompanyLOGOwww.company.com• Fraction numbers is numbers thatcan be stated as , with p and qare integers number and q are notequal to zero and q is not the factorof p• p is called numerator and q is calleddenominator.NumeratorDenominator
8. 8. CompanyLOGOwww.company.comThe cake is divided into4 equal parts. So, apart shows part ofcake.The circle is dividedinto 4 equal parts.So, a part showspart of circle.
9. 9. CompanyLOGOwww.company.comEQUIVALENT FRACTION
10. 10. CompanyLOGOwww.company.com The region of circle is dividedinto some equal parts. Theshaded area are shown bynumbers beside each figure. Because the shaded area areequal, so those three fractionsare “Equivalent Fraction”
11. 11. CompanyLOGOwww.company.comLook at the relations of fractions below !From the examples beside,we can conclude that “TheEquivalent Fraction” can beobtained if numerator anddenominator from a fractionare multiplied by the samenumber
12. 12. CompanyLOGOwww.company.comLook at the relations of fractions below !From the examples beside,we can conclude that “TheEquivalent Fraction” can beobtained if numerator anddenominator from a fractionare divided by the samenumber
13. 13. CompanyLOGOwww.company.comConclusionTo determine “The Equivalent Fraction” withis used the following characteristics :OR
14. 14. CompanyLOGOwww.company.com
15. 15. CompanyLOGOwww.company.comLook at the bars on theleft.• How many parts are in eachbar?• How many parts areshadowed?
16. 16. CompanyLOGOwww.company.comSimple FractionsFractions 1/2, 2/4, and3/6 have equal values ( youcan look from the picture ).Of these fractions, ½ isthe simplest form.A fraction is called thesimplest form (simplefraction) if the GreatestCommon Factor (GCF) of thenumerator and thedenominator is 1.
17. 17. CompanyLOGOwww.company.comWrite in the simplest form !The GCF of 28 = 1, 2, 3, 4, 7, 14, 28The GCF of 56 = 1, 2, 3, 4, 7, 8, 14, 28, 56
18. 18. CompanyLOGOwww.company.comCHANGE A MIXED fraction INTOFRACTIONS AND ITS INVERSE
19. 19. CompanyLOGOwww.company.comWhat is mixed fraction?Mixed Fraction is fractions whosenumerator greater than denominator andthe denominator is not the factor ofnumerator , for exampleThose fractions can be changed intonumber consist of integer number andfraction named “mixed fraction”.
20. 20. CompanyLOGOwww.company.comChanging improper Fraction into MixedFraction• First Method• Second MethodDenominator
21. 21. CompanyLOGOwww.company.comconclusion
22. 22. CompanyLOGOwww.company.comChanging Mixed Fraction into improperFraction1 2 3 4 5 6 7 81
23. 23. CompanyLOGOwww.company.comChanging Mixed Fraction into improperFraction1. Multiple the integer with thedenominator2. Add the product of step 1 withthe numerator3. Write the fraction as1.2.3.
24. 24. CompanyLOGOwww.company.comWe can conclude that....
25. 25. CompanyLOGOwww.company.comexercise• Change this fraction into mixed fraction andconveresly
26. 26. CompanyLOGOwww.company.com
27. 27. CompanyLOGOwww.company.comComparing Two FractionsIt can be stated that is“Less Than” or writtenasIt also can be statedthat is “Greater Than”or written as42434243434243424243
28. 28. CompanyLOGOwww.company.comTherefore, suppose we havetwo fractions with equaldenominator, to state that oneis greater than or less than theother, we only need to comparethe numerators.
29. 29. CompanyLOGOwww.company.comFrom the pictures, weknow that:is “Greater Than” .Or, written asis “Less Than” . Or,written as854343858543854385
30. 30. CompanyLOGOwww.company.comLooking for the Greater and the Less1. Determine the LCMof bothdenominators.2. Express the fractionsin equal fraction thatwe get similardenominators.3. Compare thenumerator1. 4=4, 8, 12, …8=8, 16, 24, …The LCM is 82.3. So,So,8643858565 8685568586
31. 31. CompanyLOGOwww.company.comExampleArrange these fraction from the least to thegreatest5=5, 10, 15, 20, 25, 30, 35, 40, 45, …4=4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, …8=8, 16, 24, 32, 40, 48, …LCM of denominators is 40. So, we have the equalfractioon:85,43,52402585403043401652By comparing the numerator, we get thearrangement from the least to thegreatest is43,85,52
32. 32. CompanyLOGOwww.company.comWRITE A FRACTION IN A DECIMALOR A PERCENT FORM
34. 34. CompanyLOGOwww.company.com• A fraction can also be expressed as decimal.• Similarly, a decimal can be expressed as a fraction.How can it be?
35. 35. CompanyLOGOwww.company.comHow to change fractional intodecimal forms? Conversely,How to convert decimal intofractional forms?
36. 36. CompanyLOGOwww.company.comTo convert Fractional into Decimal Forms• Fractions can be changed into decimal by changing itsdenominator into 10, 100, 1000, etc.example:Such a number as0.4 is calleddecimal and read“zero point four”.
37. 37. CompanyLOGOwww.company.comChanging Decimal into Fractional Forms• By reversing order of process in abovementionedproblems, fraction of any decimal form can be obtainedExample:
38. 38. CompanyLOGOwww.company.com• How about the denominator is difficult to change into 10,100, 1000, etc?Example:Therefore, to change the fraction intodecimal form, common division is made.Beside that, you can get the calculator toget decimal value .
39. 39. CompanyLOGOwww.company.comExercise:Change the following fractions into decimal form andchange the following decimals into fraction form
40. 40. CompanyLOGOwww.company.comPERCENTAGE
41. 41. CompanyLOGOwww.company.comLook at the article on the leftIn this article, it iswritten 18% and 60-70%. Do you knowwhat percentage is? Ifyou compare anumber to 100, thenyou will have apercentage.
42. 42. CompanyLOGOwww.company.comHow to change fractional intopercent forms? Conversely,How to change percent intofractional forms?
43. 43. CompanyLOGOwww.company.comForming Fractions into Percentage%7543%2541%5021HowCouldIt be?
44. 44. CompanyLOGOwww.company.comHow to change fraction into percentage?1. Change the fraction intodecimal form2. Multiple the product with100%75,043%75%10075,0Now, we have knownthat %7543
45. 45. CompanyLOGOwww.company.comHow to Change Percentage into Fraction?1. Divide the percentagewith 100% to getdecimal form2. Change the decimalform into fraction1.2.Factor of 5 are 5 and 1Factor of 10 are 1, 2, 5, and10So, the GCD of 5 and 10 is 51055,02151055105We Get21%505,0%100%50%100%50
46. 46. CompanyLOGOwww.company.com
47. 47. CompanyLOGOwww.company.comFractional Addition by FractionExample 1:Solution:1. Drawing of circle2. Drawing of circle
48. 48. CompanyLOGOwww.company.comFrom those picture, we can conclude that,the result of fraction addition that has samedenominator can be gotten by adding thenumerator, while the denominator is same.For every fractions and with b ≠ 0, so
49. 49. CompanyLOGOwww.company.comBy using number lineSo, 0
50. 50. CompanyLOGOwww.company.comExample 2:Solution:1. Find the LCM of 2 and 32= 2, 4, 6, 8,…3= 3, 6, 9, 12,…2. Express the fractions in equal fraction that we get similardenominator,3. Add the numerator and get the result
51. 51. CompanyLOGOwww.company.comIf the fractions that will be addedhas different denominator, firstly wemust make it same by usingLCM(Least Common Multiplication)from its denominator
52. 52. CompanyLOGOwww.company.comAdding Mixed Fraction1. Change the denominatorof the fractions2. Express the fractions inequal fraction that weget similardenominators.3. Add the numerator andget the result1.2.The multiple of 4 are 44, 8, 12, …8 8, 16, 24, …The LCM is 83.
53. 53. CompanyLOGOwww.company.comEXERCISESFind the addition of fractions below:1.2.3.4.
54. 54. CompanyLOGOwww.company.comThe Properties of Addition inFractions
55. 55. CompanyLOGOwww.company.comCommutativeFor example:So, =
56. 56. CompanyLOGOwww.company.comFor any fraction and with b≠0 and q≠0,appliesit is called commutative in addition
57. 57. CompanyLOGOwww.company.com• Example:
58. 58. CompanyLOGOwww.company.comAssociative PropertiesFor any fractions , , and with b, d, f ≠ 0 applies:
59. 59. CompanyLOGOwww.company.com
60. 60. CompanyLOGOwww.company.comAni found parts of a cake on the table. Then sheate part of the cake. What part of the cakeremained?
61. 61. CompanyLOGOwww.company.comFor any fractions and with b≠ 0, so
62. 62. CompanyLOGOwww.company.comSubtracting Unlike FractionsSolveSolution:1. Find the LCM of 2 and 32= 2, 4, 6, 8, …3= 3, 6, 9, 12,…the LCM is 62. Express the fractions in equalfraction that we get similardenominators,3. Find the result
63. 63. CompanyLOGOwww.company.comFrom that example, we can concludethat subtract unlike fractions, you have toconvert the fractions to like fractions first byusing the Least Common Multiple (LCM) ofthe denominators.
64. 64. CompanyLOGOwww.company.comSubtracting Mixed NumbersCalculateSolution:1. Convert the mixedfractions into commonfractions2. Find the LCM of 3 and 53= 3, 6, 9, 12, 15,…5= 5, 10, 15, 20,…3. Express the fractions intoequivalent fractions, so weget same denominator4. Find the result1.2. The LCM is 153. ,4.
65. 65. CompanyLOGOwww.company.comExercisesFind the result of fractions subtraction
66. 66. CompanyLOGOwww.company.comMultiplication of Fraction
67. 67. CompanyLOGOwww.company.comMultiplying a Whole Number by a FractionExample:Student A, B, and C will make handicraft. Each ofthem needs of ribbon. How many meter ofribbon that are need?Solution:A B CSO, it can be written as:
68. 68. CompanyLOGOwww.company.comFrom the example, we can conclude that awhole number multiply by a fraction is awhole number multiply with the numeratorand the denominator is exist or can bedenoted:
69. 69. CompanyLOGOwww.company.comMultiplying a Fraction by a Whole NumberExample:Ani has 5 meters of ribbon. m of ribbon will bemake a flower. How many meter of ribbon that isneeded to make a flower?Solution:1m 1m 1m 1m 1mBased on the picture m of 5 m is 1 m or
70. 70. CompanyLOGOwww.company.comMultiplying a Fraction by a FractionExample:My mother has parts of chocolate, then my mother want to presentits of chocolate. How many part of chocolate that my motherpresent?Solution:fold the shaded area thatrepresentBased on the picture there are 1 little fold from 2 flod.So
71. 71. CompanyLOGOwww.company.comBased on the example, to multiply a fraction with afraction, multiply the numerator and then multiply thedenominator or can be written as where b≠ 0 and d≠0.
72. 72. CompanyLOGOwww.company.comMultiplying a whole number and a fraction1111
73. 73. CompanyLOGOwww.company.comMultiplication of Fractions{ {{
74. 74. CompanyLOGOwww.company.comDraw a quadrilateral with a length of cm and a width ofcm as shown in the following figure.1 1111
75. 75. CompanyLOGOwww.company.comExercises
76. 76. CompanyLOGOwww.company.comThe properties of Multiplication in Fractions
77. 77. CompanyLOGOwww.company.comCommutative PropertiesFor example:so, =so, =
78. 78. CompanyLOGOwww.company.comFor any fractions and whereb≠0 and q≠ 0 applies
79. 79. CompanyLOGOwww.company.comAssociative PropertyFor any fraction , , and with b, d, f ≠ 0 can bestated
80. 80. CompanyLOGOwww.company.comDistributive PropertyFor any fraction , , and with b, d, f ≠ 0 can bestated:
81. 81. CompanyLOGOwww.company.com
82. 82. CompanyLOGOwww.company.comDivision FractionsHow to solve 8 : 2Solution:Suppose there 8 marblesSuppose the 6 chocolates are given to your friends. Each of them will get 1chocolate. How many people will get the chocolates?Answer:written as 6: 1 = 6
83. 83. CompanyLOGOwww.company.comSuppose the 3 piece of papers are divided so that each ofyour friends gets piece of paper. How many people willget the piece of paper?Answer:It means thatSo there are 6 people who get a half piece of paper.
84. 84. CompanyLOGOwww.company.comFrom the example, we can conclude thatnatural number divided by a fraction can bedenoted as:
85. 85. CompanyLOGOwww.company.comproof3: =Solution:3: can be written as a fraction, where 3 as numerator andas denominator.
86. 86. CompanyLOGOwww.company.commy mother has three-fourth of sugar. It will be made a cake.If one recipe needs a half of sugar. How many recipe canbe made?Solution:Draw a bar that represent three-fourth.kg can be maderecipekg can be made 1recipe recipeSo
87. 87. CompanyLOGOwww.company.comFor any fractions and where b, c, d ≠ 0,÷ = × applies.
88. 88. CompanyLOGOwww.company.comDividing mixed numbersCalculateSolution:Change the mixed numbers.find the product
89. 89. CompanyLOGOwww.company.comexercises1.2.3.4.
90. 90. CompanyLOGOwww.company.comAPPLICATION IN DAILY LIFE
91. 91. CompanyLOGOwww.company.comExamples1. Nindya went to his office bycar. His office is 10 km fromhis house. the time needed tobe arrived is 2 hours.if velocity (v) is stated asdistance (s) per time (t),What is the velocity of hercar?1.So, the velocity is 50km/h502100vvtsv
92. 92. CompanyLOGOwww.company.com2. Feni’s mother has acake. She divide it intotwo equal parts and shegive one part for Feni.But, feni has threefriends.2. Feni’s mother has a cakeand it divided into two.And one part for feni. So,Feni’s isFeni has three friends. So, eachfriend get:21613121321
93. 93. CompanyLOGOwww.company.com